Correlate Fatigue Crack Growth Research Articles

Quasi-In Situ Observation of the Microstructural Response during Fatigue Crack Growth of Friction Stir Welded AA2024-T4 Joint.

The reliability of friction stir welded joints is a critical concern, particularly given their potential applications in the aerospace manufacturing industry. This study offers a quasi-in situ observation of the microstructural response during fatigue crack growth (FCG) of a friction stir welded AA2024-T4 joint, aiming to correlate fatigue crack growth behavior with mechanical properties investigated using electron backscatter diffraction (EBSD). Notched compact tension (CT) specimens corresponding to the morphology of the stir zone (SZ), advancing side (AS), and retreating side (RS) were meticulously designed. The findings indicate that the welding process enhances the joint's resistance to fatigue crack growth, with the base metal exhibiting a shorter fatigue life (i.e., ~105 cycles) compared to the welding zones (SZ ~ 3.5 × 105 cycles, AS ~ 2.5 × 105 cycles, and RS ~ 3.0 × 105 cycles). Crack propagation occurs within the stir zone, traversing refined grains, which primarily contribute to the highest fatigue life and lowest FCG rate. Additionally, cracks initiate in AS and RS, subsequently expanding into the base metal. Moreover, the study reveals a significant release of residual strain at the joint, particularly notable in the Structural-CT-RS (Str-CT-RS) sample compared to the Str-CT-AS sample during the FCG process. Consequently, the FCG rate of Str-CT-AS is higher than that of Str-CT-RS. These findings have significant implications for improving the reliability and performance of aerospace components.

Infrared thermography-based evaluation of the elastic-plastic J-integral to correlate fatigue crack growth data of a stainless steel

The elastic-plastic J-integral is adopted to correlate fatigue crack growth data of ductile metals. An analytical link is known to exist between the J-integral and the strain energy density averaged in a control volume embracing the crack tip. On the other hand, the strain energy fluctuation is the source of temperature variations close to a fatigue crack tip of a metal material; hence the possibility to measure the J-integral from infrared thermographic scanning at the crack tip is envisaged and it is the focus of this paper. It is proposed that the elastic component of the J-integral is derived from a thermoelastic stress analysis, while the plastic component of the J-integral is derived from the heat energy loss. An analytical expression is formalised to apply this novel approach. Therefore, the elastic-plastic J-integral range was evaluated starting from infrared temperature maps measured in situ during crack propagation tests of AISI 304L stainless steel specimens. The range of the infrared thermography-based J-integral correlated well the crack growth data generated in small as well as large scale yielding conditions. Finally, the experimental values of the J-integral were successfully compared with the corresponding numerical values obtained from elastic-plastic finite element analyses.

Net-section based approach for fatigue crack growth characterization using compact tension specimen: Physical correlation of mean stress or stress ratio effects

A new approach is demonstrated here for the correlation of fatigue crack growth (FCG) data, generated using compact tension (CT) specimens, for various mean stress levels or stress ratios (R) of testing. The approach uses the change in the cyclic strain energy of the net-section as a parameter to correlate fatigue crack growth rates. The derivation of the change in net-section strain energy, for the CT specimen, is demonstrated here on the basis of energy principles of solid mechanics. The total change in net-section strain energy is determined as the sum of the changes in the tension and the bending strain energy components, arising from the tensile stress and the bending moment acting on the net-section of the CT specimen. This leads to a compact physical equation for the change in cyclic strain energy, which is expressed as a direct function of applied cyclic load level, crack length, stress ratio, and specimen dimensions. Extensive experimental evaluations, using the data for steels, copper and titanium alloys, were conducted and are presented here to show that the change in net-section strain energy can successfully correlate the fatigue crack growth for various stress ratios or mean stress levels. The present work provides a new direction for physically-based characterizations of fatigue crack growth data generated using CT specimens.

Mechanics of fatigue crack growth under large-scale plasticity: A direct physical approach for single-valued correlation of fatigue crack growth data

The major challenge in the mechanics of elastic-plastic fatigue crack growth is to find a physically based driving force parameter to correlate the crack growth rates under different loading conditions. Specifically, a parameter that can provide single-valued correlation of crack growth rates, in stress-controlled and strain-controlled fatigue, is needed. Approaches of the past used either cyclic strain (strain intensity factor) or nonlinear-fracture-mechanics based (cyclic J-integral, ΔJ) parameter, to correlate fatigue crack growth. The validity of these approaches, however, has not been established. Further, the J-integral based approach requires experimental load-deflection curves, recorded after every crack length increment, and geometry-correction factors, which are numerically determined and complicated. In the present work, a physically based approach, based on thecumulative change in the cyclic strain energy of the net-section, is used to develop new parameters that can successfully correlate fatigue crack growth behavior in a variety of loading situations. The driving force parameter, capturing the change in the net-section cyclic strain energy, is determined analytically from elastic-plastic behavior of material and from the relative sizes of cracked and uncracked sections in the crack plane. Load-deflection measurements, geometric correction factors, or numerical methods are not needed in the present approach. Remarkably, excellent correlations of fatigue crack growth, in a variety of specimen geometries and for various stress/strain levels, have been found in both stress- or strain-controlled fatigue conditions. This work, extending the author’s earlier works for elastic fatigue crack growth, validates that the change in net-section strain energy is a fundamental quantity in the mechanics of fatigue crack growth.

An approach to correlate fatigue crack growth rate with S-N curve for an aluminum alloy LY12CZ

By considering fatigue crack growth (FCG) as the consequence of fatigue fracture of crack front, the correlation between crack growth rate and S-N curve has been investigated. A method to calculate the fatigue life of crack front from the S-N curve has been developed by taking the initial damage at the crack front into account. It is found that the effect of initial damage on fatigue life can be approximately expressed by a parallel shift of S-N curve in bi-logarithmic graph. Thus, crack growth rate curve corresponding to an initial damage at crack front, can also be obtained by a parallel shift of the base curve, which can be calculated from the imaginary fatigue life of crack front without initial damage. The shift distance is dependent on the initial damage at crack front, and can be determined by just one or several experimental results of crack growth. Thereby, the test numbers to obtain crack growth curve can be reduced greatly by adopting this correlation.

A validation of a modified Paris relation for fatigue delamination growth in unidirectional composite laminates

Abstract The aim of this paper is to provide evidence on the validation of a modified Paris relation in fatigue crack growth with fibre bridging. Energy principles were first applied to investigate energy release in fatigue delamination growth. A comparison between the Paris and the modified Paris relations was completed subsequently. The application of the Paris relation can artificially cause different resistance curves of fatigue delamination with fibre bridging, violating the hypothesis of similitude and the energy dissipation results. However, the use of the modified Paris relation can result in a master resistance curve, which is physically consistent with the law of similitude and the energy release regulations. This derives from using an appropriate similitude parameter in data reduction. It is therefore reasonable to use the strain energy release rate (SERR) actually applied on the crack front, rather than the total applied SERR, as similitude to correlate fatigue crack growth. The master resistance curve was finally employed to predict fatigue results from literature. Acceptable agreement between predictions and experiments was achieved, validating the effectiveness of the modified Paris relation in determining fatigue crack growth with fibre bridging.

New approach for the correlation of fatigue crack growth in metals on the basis of the change in net-section strain energy

A new approach to correlate fatigue crack growth data of metals on the basis of the change in net-section strain energy is presented. Extensive experimental data, including some historically significant fatigue crack growth data, generated using center-cracked (CCT) and single-edge notched (SENT) tension specimens, are used to demonstrate this correlation. It is shown that this correlation, quite remarkably, is as strong as that based on the stress intensity factor range (ΔK) in fracture mechanics. The reason for this surprising similarity is explored using the analysis of the net-section stress increase in fracture mechanics specimens. It is found that the actual role of the finite-width-correction factor in fracture mechanics is to create the stress amplification effect on the finite specimen, having a given crack length, to produce the same K as that of an infinite specimen. The present work demonstrates that the phenomenon of fatigue crack growth can be easily understood on the basis of the accumulated change in net-section strain energy which directly relates to the accumulated work done at the loading ends, which determines the rate of fatigue crack growth. It is a simpler and a physical approach for the accurate description of fatigue crack growth behavior of metals. The approach simultaneously validates the use of fracture mechanics parameters (∆K) for fatigue crack growth, by providing the insight that the physical meaning of stress intensity factor is embedded in the change in the net-section strain energy.

A universal functional for the physical description of fatigue crack growth in high-cycle and low-cycle fatigue conditions and in various specimen geometries

A simple universal functional is shown here to correlate fatigue crack growth data of a wide variety of materials (metals, polymers), test conditions (high-cycle and low-cycle fatigue), and specimen configurations (tension and bending). The proposed functional is a power law that relates the normalized remaining ligament size to the normalized remaining fatigue life in a cyclically loaded specimen. The functional evolved from the idea that at any stage during fatigue, the remaining fraction of cycles required to fracture the specimen, completely, depends on the remaining fraction of section to be broken by the fatigue crack before that final fracture. More importantly, the surrogate form of the functional is shown to provide excellent descriptions of the raw crack-length-versus-cycles data in fatigue crack growth. The functional provides a new physical basis to characterize fatigue crack growth in materials and is promising for extensions in to more complicated fatigue loading conditions.

Fatigue Crack Closure due to Surface Roughness and Plastic Deformation

Crack closure is an important factor affecting fatigue crack growth in high strength alloy materials. Plasticity is known to be the main driver of closure, but in some materials and at some stages other mechanisms such as fracture surface roughness and debris accumulation are also important. Analytical models based on the plasticity induced closure concept have been very successful in correlating fatigue crack growth rates and lives for a range of materials under constant amplitude and spectrum loading. However, extreme values of plastic constraint factors, significantly lower than those determined from three dimensional finite element studies on similar geometry, are needed to achieve good correlation with experimental results, particularly for materials which exhibit rough and tortuous fatigue surfaces. One such material investigated here is β-annealed Ti-6Al-4V titanium alloy. The aim of this paper is to further develop, apply and evaluate a crack closure model which combines roughness and plasticity induced closure, incorporating experimental measurements of fracture surface roughness from tests on Eccentrically Loaded Single Edge-Notch Tension (ESE(T)) specimens. The model was first proposed by Zhang et al. 2002 for short cracks in 2000 series Aluminium Alloy. The model was evaluated here for physically longer cracks in the Titanium Alloy material. Accurate surface profile and roughness measurements were made using an optical 3-D profiler with a vertical resolution of better than 0.15 μm. Verification of the proposed model was carried out by comparing the model prediction with the closure measurements by back-face strain compliance using the pin-loaded ESE(T) specimens. Results from the roughness model were then compared with results from the FASTRAN analytical crack closure code. Analysis using this new approach, with plastic constraint factors more closely aligned with the values determined from independent classical and three dimensional finite element studies, provide a solid basis from which to implement the approach in FASTRAN.

Correlation of one-dimensional fatigue crack growth at cold-expanded holes using linear fracture mechanics and superposition

This work assesses the ability of linear elastic fracture mechanics (LEFM) with superposition to correlate the growth of one-dimensional fatigue cracks at cold-expanded open holes under constant amplitude loading. Care is taken in the work to accurately: control the test setup to ensure one-dimensional crack growth, determine residual stress in the coupons, measure crack growth, determine the fatigue crack growth rate (FCGR), compute stress intensity factors, and correlate fatigue crack growth rate with stress intensity factor range Δ K and stress ratio R. The work used long dog-bone coupons having a gage section 38.1 mm wide and a centrally located 7.09 mm diameter hole. The coupons were fabricated from 2.03 mm thick 7075-T6 sheet. The small coupon thickness and alignment of the loading fixture to eliminate bending resulted in one-dimensional crack growth. Residual stress due to cold expansion (CX) was measured using the contour method, as a function of position on the crack plane. Residual stress measurements gave typical results for the average residual stress field, with near-yield compression at the hole giving way to tension further out. Measurements on multiple coupons showed ±10% variability in residual stress. Crack growth behavior of multiple as-machined (AM) coupons (without CX) tested at R of 0.1 or 0.5 agreed with earlier results published in the literature. The scatter in lifetime, defined as the range of lifetime divided by the average lifetime, was less than 30% in the AM coupons. Crack growth behavior of multiple CX coupons tested at the same two applied stress ratios was consistent with predictions by linear superposition, where the predictions used a correlation for fatigue crack growth rate as a function of Δ K and R based on crack closure concepts and a piecewise log–log fit to FCGR versus Δ K eff data from tests of non-residual stress bearing material and from the literature. Scatter in lifetime of CX coupons was 152% at R = 0.1 and 69% at R = 0.5. While the scatter in CX coupon lifetime is considerably greater than for AM coupons, it is found consistent with the observed 10% variability in residual stress. The work therefore demonstrates the ability of LEFM with superposition to accurately correlate the behavior of coupons with and without residual stresses.

Reflections on identifying the real Δ Keffective in the threshold region and beyond

The use of the crack tip stress intensity factor, K, has survived almost 50 years as the key parameter correlating fatigue crack growth. As time past the range of the stress intensity, Δ K, was recognized as causing alternating plasticity at the crack tip. The threshold level for Δ K was discovered. Further, the occurrence of crack closure was noted which affected the Δ K for different load ratios, R of cyclic loading. The ASTM method of counting the linear part of the load displacement for determining Δ K open was found to understate the Δ K effective, which correlates data for different load ratios. One approach to adjust for this problem is the “Partial Closure Model”, where the closure only occurs away from the crack tip. Here it will be discussed that such a model leads to a universal growth law. Moreover, this law shows application in estimating the order of magnitude of crack growth life (<10 7 cycles) for example with very high cycle fatigue (>10 9 cycles). Some advances in this application will also be cited.

A study of the stress ratio effects on fatigue crack growth using the unified two-parameter fatigue crack growth driving force

A unified two-parameter fatigue crack growth driving force model was developed to account for the residual stress and subsequently the stress ratio effect on fatigue crack growth. It was found that the driving force should be expressed as a combination of the maximum stress intensity factor, K max, and the stress intensity range, Δ K, corrected for the presence of the residual stress. As a result, the effects of residual stresses manifest themselves in changes of the applied maximum stress intensity factor and the applied stress intensity range. A two-parameter function of the maximum total stress intensity factor, K max,tot, and the total stress intensity range, Δ K tot, was proposed to model the fatigue crack growth rate data obtained at various R-ratios. Based on the analysis, the unified two-parameter driving force, Δ κ = K max,tot p Δ K tot ( 1 - p ) , was derived accounting for the mean stress or the stress ratio effect on fatigue crack propagation. It was shown that the two-parameter driving force, Δ κ = K max,tot p Δ K tot 0.5 , was capable of correlating fatigue crack growth data obtained under a wide range of load ratios and fatigue crack growth rates spanning from the near threshold to the high growth rate regime. The model was successfully verified using a wide range of fatigue crack growth data obtained for Al 2024-T351 aluminium alloy, St-4340 steel alloy and Ti–6Al–4V titanium alloy with load ratios, R, ranging from −1 to 0.7.

The importance of compressive stresses on fatigue crack propagation rate

This paper is concerned with the importance of compressive stresses on crack propagation rate. In a previous paper, namely ‘Crack Closure Inadequacy at Negative Stress Ratios’, Int. Journal of Fatigue, 26, 2004, pp. 241–252, was demonstrated the inadequacy of the crack closure concept and Δ K eff, at a negative stress ratio, R=−1, to predict crack propagation rate. It that paper was verified that, at negative stress ratios, crack closure changes with P max, for the same R ratio. The main conclusion was about plastic properties and mainly cyclic plastic properties, the Bauschinger effect included, on crack propagation when compressive stresses exist. It was then suggested that in the place of the crack closure concept, another concept based on plasticity should be used to explain fatigue crack propagation. In this paper, instead of working with the same negative R ratio ( R=−1), a study on the behavior of crack propagation rate as a function of R ratio, from negative to positive stress ratios, is made. Both the effect of P max and of R ratio is taken into consideration. Measurements of roughness and of crack opening loads are made, in order to verify their influence on crack propagation rate. Different materials, in order to cover different cyclic plastic properties and different sensitivities to roughness are studied ( Ck45-cyclic hardening; Ti6 Al4 V-cyclic softening, and aluminum, Al 7175-cyclically neutral) are studied. Aluminium alloys and titanium alloys are considered to be sensitive to roughness induced crack closure (RICC) while steels are more dependent on plastic properties (PICC). In this study it is emphasized the importance of the compressive part of the cycle, and of cyclic plastic properties, on crack propagation rate. It is reassessed the inadequacy of crack closure concept and Δ K eff to describe crack propagation rate, at negative stress ratios. It is also verified that models based solely on extrinsic properties of materials, like d a/d N−Δ K or d a/d N−Δ K ( K max) should also incorporate intrinsic properties of the materials in order to properly correlate fatigue crack growth.

Closure‐free biaxial fatigue crack growth rate and life prediction under various biaxiality ratios in SAE 1045 steel

Biaxial fatigue tests were performed on thin‐walled tubular 1045 steel specimens in a test fixture that applied internal and external pressure and axial load. There were two test series, one in which constant amplitude fully reversed strains (CAS) were applied and another in which large periodic compressive overstrain (PCO) cycles causing strains normal to the crack plane were inserted in a constant amplitude history of smaller strain cycles. Ratios of hoop strain to axial strain ofλ = −1, −0.625, −νand +1 were used in each test series. Fatigue crack growth behaviours under CAS and PCO histories were compared, and revealed that the morphology of the fracture surface near the crack tip and the crack growth rate changed dramatically with the application of the compressive overstrains. When the magnitude of the compressive overstrains was increased, the height of the fracture surface irregularities was reduced as the increasing overstrain progressively flattened the fracture surface asperities near the crack tip. The reduced asperity height was accompanied by drastic increases in crack growth rate and decreases in fatigue life.Using a pressurizing device attached to the confocal scanning laser microscope (CSLM), crack opening measurements were obtained. Crack opening measurements showed that the biaxial cracks were fully open at zero internal pressure for block strain histories containing in‐phase PCO cycles of yield stress magnitude. Therefore, for the shear‐strained samples, there was no crack face interference and the strain intensity range was fully effective. For PCO tests (with biaxial strain ratios of −0.625 and +1), effective strain intensity data were obtained from tests with positive stress ratios for which cracks did not close. A number of strain intensity parameters derived from well‐known fatigue life parameters were used to correlate fatigue crack growth rates for the various strain ratios investigated. Predicted fatigue lifetimes based on a fatigue crack growth rate prediction program using critical shear plane parameters showed good agreement with the experimental fatigue life data.

EFFECT OF SPECIMEN THICKNESS ON FATIGUE CRACK GROWTH BEHAVIOUR UNDER CONSTANT AND VARIABLE AMPLITUDE LOADING

Mode I fatigue crack growth behaviour was experimentally investigated under constant and following the application of a single spike overload. Different specimen thicknesses were investigated at different overload ratios. A previously developed crack tip deformation model to correlate fatigue crack growth behaviour following k a single overload cycle was used to correlate that behaviour for different specimen thicknesses. It was found that the effect of specimen thickness on the fatigue crack growth behaviour under constant amplitude of loading is marginal especially at growth rates greater than le mm/cycle. The retardation due to the application of a tensile single overload decreases with the increase in specimen thickness. Good agreement between relevant experimental results and those predicted using three dimensional crack tip deformation parameter was found.

Effect of Stress Ratio on Fatigue Crack Growth in 95Pb-5Sn Solder

The stress ratio effect on the fatigue crack growth behavior of 95Pb-5Sn solder has been investigated. It is found that both ΔJ and ΔK can correlate fatigue crack growth data well, which means that the crack growth behavior of the 95Pb-5Sn solder under the frequency of 10 Hz was dominantly cyclic dependent. The da/dN-ΔJ relationship can be expressed as: da/dN=1.1×10−11s˙ΔJ1.45. Low level of crack closure was found only in the near-threshold region. Except in this region, no crack closure was observed in the present test conditions. Both transgranular and intergranular fractures were observed on fracture surfaces: the former was dominant in most test conditions and the latter was dominant at the high stress ratio of 0.7. Striations and striation-like features were also found. Many slip bands and cavities along the grain boundary were observed on the crack wake and ahead of the crack tip in the high crack growth rate region.

An energy approach to crack closure

Crack closure is analyzed using an energy approach whereby it is shown that crack closure does not completely shield the input mechanical energy to the crack tip at a load below the crack opening load Pop if the compliance below Pop is non-zero. An equivalent shielding stress intensity range is defined by the energy release rate against crack closure. From this energy standpoint, the true effective stress intensity range should be defined as ΔKeff=Kmax−χKop, where χ is the shielding factor. The conventional definition (ΔKeff=Kmax−Kop) is equivalent to the new definition only when the compliance below Pop is zero such that χ=1, i.e., for a fully closed crack. The corrected ΔKeff is found to be effective in correlating fatigue crack growth rates (FCGRs) generated in 8090-T8771 aluminum-lithium alloy with and without crack closure. In contrast, the conventional ΔKeff fails to reconcile the FCGR data within an acceptable scatter band.

Analysis of fatigue crack growth in a rubber-toughened epoxy resin: effect of temperature and stress ratio

Fatigue crack propagation in a rubber-toughened epoxy resin was studied at different test temperatures (−40 to 60°C) and stress ratios (0.05 to 0.70) using single edge-notched specimens at a frequency of 5 Hz. Fatigue crack propagation rates ( da dN ) were plotted against the stress-intensity factor amplitude ( ΔK) in accordance with the Paris power-law equation. For a given stress ratio da dN was not sensitive to variations in test temperature. But for a given temperature da dN increased with stress ratio. Using the Williams' two-stage line zone model to analyse these experimental data, it was shown that the main failure process was due to shear plastic flow at the crack tip. The fatigue stress and the closure stress-intensity factor both decreased with increasing temperature, implying that more severe damage had occurred at higher testing temperatures. The experimental data were also analysed in terms of a new fatigue model, which considers the accumulation of damage due to cyclic plastic strain in the reversed plastic zone similar to the Coffin-Manson law and crack closure due to residual plastic stretch at the crack wake. There was good agreement between theory and experiment, suggesting a simpler way to correlate fatigue crack growth rates in this and other polymeric materials.

A rapid method for measurement of rolling contact fatigue limit of case-hardened gear materials: Jiang, B, and Shao, E. ASTM J. Testing Eval. Sept. 1990 18, (5), 328–331

A unified two-parameter fatigue crack growth driving force model was developed to account for the residual stress and subsequently the stress ratio effect on fatigue crack growth. It was found that the driving force should be expressed as a combination of the maximum stress intensity factor, Kmax, and the stress intensity range, ΔK, corrected for the presence of the residual stress. As a result, the effects of residual stresses manifest themselves in changes of the applied maximum stress intensity factor and the applied stress intensity range. A two-parameter function of the maximum total stress intensity factor, Kmax,tot, and the total stress intensity range, ΔKtot, was proposed to model the fatigue crack growth rate data obtained at various R-ratios. Based on the analysis, the unified two-parameter driving force, Δκ=Kmax,totpΔKtot(1-p), was derived accounting for the mean stress or the stress ratio effect on fatigue crack propagation. It was shown that the two-parameter driving force, Δκ=Kmax,totpΔKtot0.5, was capable of correlating fatigue crack growth data obtained under a wide range of load ratios and fatigue crack growth rates spanning from the near threshold to the high growth rate regime.The model was successfully verified using a wide range of fatigue crack growth data obtained for Al 2024-T351 aluminium alloy, St-4340 steel alloy and Ti–6Al–4V titanium alloy with load ratios, R, ranging from −1 to 0.7.

Driving forces for composite interface fatigue cracks

The relevant Fracture mechanics parameter for representing the crack extension driving force of interface fatigue cracks has been studied both analytically and experimentally. Using the oscillatory stress singularities for open-tip interface cracks, an equivalent stress intensity range, defined in terms of the y-integral and evaluated on the basis of the applied loads, is proposed and shown to correlate fatigue crack growth data of interface cracks in fiber-reinforced composites. Two complimentary procedures for determining the local ΔK of interface fatigue cracks using experimental crack opening displacements data are presented. Differences between the local and global ΔKare thought to be due to residual stresses which originated during fabrication.